Details Page for 0.7172

Complete Solution is Known:

MSV File: q-0.7172.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₀₇(0.7172):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z | a²=1, b²⁵=b²³, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, b²e=ab⁷, ce=b⁷, de=b⁹, e²=b¹⁰, b³f=ab⁹, cf=ab²f, df=b¹⁰, ef=b¹¹, f²=b¹², b⁴g=ab¹¹, cg=ab²g, dg=b¹¹, eg=b¹², fg=b¹³, g²=b¹⁴, b⁵h=ab¹³, ch=ab²h, dh=ab⁴h, eh=b¹³, fh=b¹⁴, gh=b¹⁵, h²=b¹⁶, b⁶i=ab¹⁵, ci=ab²i, di=ab⁴i, ei=ab⁵i, fi=b¹⁵, gi=b¹⁶, hi=b¹⁷, i²=b¹⁸, b⁷j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=ab⁵j, fj=ab⁶j, gj=b¹⁷, hj=b¹⁸, ij=b¹⁹, j²=b²⁰, b⁸k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁵k, fk=ab⁶k, gk=ab⁷k, hk=b¹⁹, ik=b²⁰, jk=b²¹, k²=b²², b⁹l=ab²¹, cl=ab²l, dl=ab⁴l, el=ab⁵l, fl=ab⁶l, gl=ab⁷l, hl=ab⁸l, il=b²¹, jl=b²², kl=b²³, l²=b²⁴, b¹⁰m=ab²³, cm=ab²m, dm=ab⁴m, em=ab⁵m, fm=ab⁶m, gm=ab⁷m, hm=ab⁸m, im=ab⁹m, jm=b²³, km=b²⁴, lm=b²³, m²=b²⁴, b¹¹n=ab²³, cn=ab²n, dn=ab⁴n, en=ab⁵n, fn=ab⁶n, gn=ab⁷n, hn=ab⁸n, in=ab⁹n, jn=ab¹⁰n, kn=b²³, ln=b²⁴, mn=b²³, n²=b²⁴, b¹⁰o=b⁹n, co=ab²o, do=ab⁴o, eo=ab⁵o, fo=ab⁶o, go=ab⁷o, ho=ab⁸o, io=ab⁹o, jo=ab⁹n, ko=ab¹⁰n, lo=b²³, mo=b²⁴, no=b²³, o²=b²⁴, b⁹p=b⁸o, cp=ab²p, dp=ab⁴p, ep=ab⁵p, fp=ab⁶p, gp=ab⁷p, hp=ab⁸p, ip=ab⁸o, jp=ab⁹o, kp=ab⁹n, lp=ab¹⁰n, mp=b²³, np=b²⁴, op=b²³, p²=b²⁴, b⁸q=b⁷p, cq=ab²q, dq=ab⁴q, eq=ab⁵q, fq=ab⁶q, gq=ab⁷q, hq=ab⁷p, iq=ab⁸p, jq=ab⁸o, kq=ab⁹o, lq=ab⁹n, mq=ab¹⁰n, nq=b²³, oq=b²⁴, pq=b²³, q²=b²⁴, b⁷r=b⁶q, cr=ab²r, dr=ab⁴r, er=ab⁵r, fr=ab⁶r, gr=ab⁶q, hr=ab⁷q, ir=ab⁷p, jr=ab⁸p, kr=ab⁸o, lr=ab⁹o, mr=ab⁹n, nr=ab¹⁰n, or=b²³, pr=b²⁴, qr=b²³, r²=b²⁴, b⁶s=b⁵r, cs=ab²s, ds=ab⁴s, es=ab⁵s, fs=ab⁵r, gs=ab⁶r, hs=ab⁶q, is=ab⁷q, js=ab⁷p, ks=ab⁸p, ls=ab⁸o, ms=ab⁹o, ns=ab⁹n, os=ab¹⁰n, ps=b²³, qs=b²⁴, rs=b²³, s²=b²⁴, b⁵t=b⁴s, ct=ab²t, dt=ab⁴t, et=ab⁴s, ft=ab⁵s, gt=ab⁵r, ht=ab⁶r, it=ab⁶q, jt=ab⁷q, kt=ab⁷p, lt=ab⁸p, mt=ab⁸o, nt=ab⁹o, ot=ab⁹n, pt=ab¹⁰n, qt=b²³, rt=b²⁴, st=b²³, t²=b²⁴, b⁴u=b³t, cu=ab²u, du=ab³t, eu=ab⁴t, fu=ab⁴s, gu=ab⁵s, hu=ab⁵r, iu=ab⁶r, ju=ab⁶q, ku=ab⁷q, lu=ab⁷p, mu=ab⁸p, nu=ab⁸o, ou=ab⁹o, pu=ab⁹n, qu=ab¹⁰n, ru=b²³, su=b²⁴, tu=b²³, u²=b²⁴, b³v=b²u, cv=ab²v, dv=ab³u, ev=ab³t, fv=ab⁴t, gv=ab⁴s, hv=ab⁵s, iv=ab⁵r, jv=ab⁶r, kv=ab⁶q, lv=ab⁷q, mv=ab⁷p, nv=ab⁸p, ov=ab⁸o, pv=ab⁹o, qv=ab⁹n, rv=ab¹⁰n, sv=b²³, tv=b²⁴, uv=b²³, v²=b²⁴, b²w=bv, cw=abv, dw=ab²u, ew=ab³u, fw=ab³t, gw=ab⁴t, hw=ab⁴s, iw=ab⁵s, jw=ab⁵r, kw=ab⁶r, lw=ab⁶q, mw=ab⁷q, nw=ab⁷p, ow=ab⁸p, pw=ab⁸o, qw=ab⁹o, rw=ab⁹n, sw=ab¹⁰n, tw=b²³, uw=b²⁴, vw=b²³, w²=b²⁴, bx=w, cx=abw, dx=ab²v, ex=ab²u, fx=ab³u, gx=ab³t, hx=ab⁴t, ix=ab⁴s, jx=ab⁵s, kx=ab⁵r, lx=ab⁶r, mx=ab⁶q, nx=ab⁷q, ox=ab⁷p, px=ab⁸p, qx=ab⁸o, rx=ab⁹o, sx=ab⁹n, tx=ab¹⁰n, ux=b²³, vx=b²⁴, wx=b²³, x²=b²⁴, by=x, cy=aw, dy=abv, ey=ab²v, fy=ab²u, gy=ab³u, hy=ab³t, iy=ab⁴t, jy=ab⁴s, ky=ab⁵s, ly=ab⁵r, my=ab⁶r, ny=ab⁶q, oy=ab⁷q, py=ab⁷p, qy=ab⁸p, ry=ab⁸o, sy=ab⁹o, ty=ab⁹n, uy=ab¹⁰n, vy=b²³, wy=b²⁴, xy=b²³, y²=b²⁴, bz=y, cz=ax, dz=abw, ez=abv, fz=ab²v, gz=ab²u, hz=ab³u, iz=ab³t, jz=ab⁴t, kz=ab⁴s, lz=ab⁵s, mz=ab⁵r, nz=ab⁶r, oz=ab⁶q, pz=ab⁷q, qz=ab⁷p, rz=ab⁸p, sz=ab⁸o, tz=ab⁹o, uz=ab⁹n, vz=ab¹⁰n, wz=b²³, xz=b²⁴, yz=b²³, z²=b²⁴>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, ae, abf, ag, ab²g, abh, ab³h, ai, ab²i, ab⁴i, abj, ab³j, ab⁵j, ak, ab²k, ab⁴k, ab⁶k, abl, ab³l, ab⁵l, ab⁷l, am, ab²m, ab⁴m, ab⁶m, ab⁸m, abn, ab³n, ab⁵n, ab⁷n, ab⁹n, ao, ab²o, ab⁴o, ab⁶o, ab⁸o, abp, ab³p, ab⁵p, ab⁷p, aq, ab²q, ab⁴q, ab⁶q, abr, ab³r, ab⁵r, as, ab²s, ab⁴s, abt, ab³t, au, ab²u, abv, aw, ay}

Phi = 1 a b a 1 ab 1 ab b a b c ac ab ac ab³ b³ ab² b³ d b⁴ ab³ b⁴ e b⁵ ab⁴ b⁵ f b⁶ ab⁵ b⁶ g b⁷ ab⁶ b⁷ h b⁸ ab⁷ b⁸ i b⁹ ab⁸ b⁹ j b¹⁰ ab⁹ b¹⁰ k b¹¹ ab¹⁰ b¹¹ l b¹² ab¹¹ b¹² m b¹³ ab¹² b¹³ n b¹⁴ ab¹³ b¹⁴ o b¹⁵ ab¹⁴ b¹⁵ p b¹⁶ ab¹⁵ b¹⁶ q b¹⁷ ab¹⁶ b¹⁷ r b¹⁸ ab¹⁷ b¹⁸ s b¹⁹ ab¹⁸ b¹⁹ t b²⁰ ab¹⁹ b²⁰ u b²¹ ab²⁰ b²¹ v b²² ab²¹ b²² w b²³ ab²² b²³ x b²⁴ ab²³ b²⁴ y b²³ ab²⁴ b²³ z b²⁴ ab²³ b²⁴

Monoid Structure